Effect of π-π interaction on high-energy π-p scattering

Abstract

The object of this paper is to examine the possibility of explaining the second maximum in (π-p) scattering in the framework of the Tamm-Dancoff approximation for (π-p) interaction, by postulating a resonant π-π interaction in the isotopic spin state I=0 of the π-π system. For this purpose the Tamm-Dancoff method in pseudosclar theory, as formulated by Dyson and others, is first extended so as to include the effects of a π-π interaction. This is achieved by introducing a Green's function whose form is determined on the assumption of a zero-range π-π interaction in the state I=0 of the π-π system. The solution of the "modified" integral equation is greatly simplified by assuming the π-p interaction to be weak compared with the π-π interaction (the reasons for which are given). The total inelastic cross section is then derived by using the unitary property of the S matrix.It is found that the Tamm-Dancoff approximation is unable to explain the (π-p) maximum on the basis of the proposed model. This is contrary to the result derived by other authors, who used the impulse approximation for the interaction of the incident meson with the meson cloud surrounding the nucleon.